The explosive growth of the Internet has created a demand for high data rates for business and residential users (SOHO—small office/house office) that rely on standard analog plain old telephone systems (POTS) that use a copper wire twisted pair to carry the information. The need for high-speed access to the home is increasing due to the availability of information, data, high-bandwidth video and the like, such as from the world wide web. Because of such demand, higher speed modems are required. A multitude of competing communication technologies provide high-speed access to the home such as cable modems and digital subscriber line (xDSL) equipment. DSL equipment may utilize the existing analog POTS that uses a copper wire twisted pair to carry voice and information. Because of bandwidth limitation (4 KHz), and power limitation of the telephone network, line coding schemes are used to encode digital signals into analog signals that convey the analog information over the analog telephone network. Such line coding schemes should avoid the undesirable bandwidth or power increase.
In VDSL systems a transmit window is used to reduce the power leakage in the out-of-band regions and RFI band regions in the frequency domain. In the past, many well-known windows, such as Raised-Cosine window, Chebyshev window, Kaiser Window, Hanning Window, and Hamming Window, have been applied. However, given the strict power-mask constraints defined in the VDSL standard, all the windows mentioned above still induce severe power-leakage in the out-of-band regions and RFI band regions. This requires that many tones around the band transition areas must be turned off to reduce the power leakage. Because turning off bands reduces the lines ability to carrier information, and therefore effectively reduces bandwidth, it is less than desirable.